I have drowning as a secondary method and so it's something I've researched and tested (under controlled conditions with an unwitting assistant). The actual weight itself won't be the problem here, but instead, as pointed out above, the real problem will be when your survival instinct kicks in. At a certain point, you will unconsciously begin to thrash around and attempt to remove the weights, if any are loose they will either fall or be ripped off. I note that you're planning to take Xanax, depending on how many of those you take and your state of consciousness at the time you enter the water (you may still be conscious but not fully lucid) the usual drowning response may not kick in.
What worried me most about this method for me was more the excruciating pain and panic once I was under the water, that would no doubt be made much worse by the weights, assuming they are sufficiently secured to your body. There are ways of mitigating the pain if it's important to you, I briefly discussed some of my techniques on another thread but they are probably repeated elsewhere here as well.
It may be wise to attempt a dry run first. Attach the weights to yourself the way that you intend to and then set a timer and challenge yourself to escape from them as fast as possible. Even if you end up ripping the weights off (meaning you have to buy more straps), you've demonstrated that they're not suitable for your use and better to have to buy another set of straps or a new vest than have your attempt fail because you somehow turned into Hercules in the water and discovered that the stitchwork on your vest was poor and ripped right off...
Either way, spend some time to get this right.